<PAGE>   1
 
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 7, 1996                               /s/ CRAIG R. ANDERSSON
                                            By
 
                                                     Craig R. Andersson
<PAGE>   2
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 8, 1996                               /s/ NEIL A. ARMSTRONG
                                            By
 
                                                     Neil A. Armstrong
<PAGE>   3
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 8, 1996                                /s/ DANIEL I. BOOKER
                                            By
 
                                                      Daniel I. Booker
<PAGE>   4
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 12, 1996                              /s/ RONALD L. GALLATIN
                                            By
 
                                                     Ronald L. Gallatin
<PAGE>   5
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 8, 1996                               /s/ CHARLES C. GEDEON
                                            By
 
                                                     Charles C. Gedeon
<PAGE>   6
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 7, 1996                              /s/ ROBERT M. HERNANDEZ
                                            By
 
                                                    Robert M. Hernandez
<PAGE>   7
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 15, 1996                                /s/ LOUIS A. VALLI
                                            By
 
                                                       Louis A. Valli
<PAGE>   8
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     That, the undersigned does hereby make, constitute and appoint, Timothy G.
Rupert or L. Frederick Gieg, Jr., my true and lawful attorney-in-fact, to sign
and execute for me and on my behalf, the Annual Report on Form 10-K for the year
1995 for RMI Titanium Company, and any and all amendments thereto to be filed
with the Securities and Exchange Commission pursuant to the Securities Exchange
Act, as amended, in such form as they or any one or more of them may approve,
and to do any and all other acts which said attorney-in-fact may deem necessary
or desirable to enable RMI Titanium Company to comply with said Act and the
rules and regulations thereunder.
 
     IN WITNESS WHEREOF, I have hereunto set my hand and seal.
 
Dated: March 7, 1996                              /s/ WESLEY W. VON SCHACK
                                            By
 
                                                    Wesley W. von Schack